11—Numerical Analysis 35311.37 Derive Eq. ( 49 ).
(b) Explain why the plausibility arguments that follow it actually say something.
11.38 After you’ve done the Euclidean fit of data to a straight line and you want to do the data reduction
described after Eq. ( 54 ), you have to find the coordinate along the line of the best fit to each point. This is
essentially the problem: Given the line (~uandˆv) and a point (~w), the new reduced coordinate is theαin~u+αˆv
so that this point is closest to ~w. What is it? You can do this the hard way, with a lot of calculus and algebra,
or you can draw a picture and write the answer down.
11.39 Data is given as (xi,yi) ={(1,1),(2,2),(3,2)}. Compute the Euclidean best fit line. Also find the
coordinates,αi, along this line and representing the reduced data set.
Ans:~u= (2, 5 /3) ˆv= (0. 88167 , 0 .47186) α 1 =− 1. 1962 α 2 = 0. 1573 α 3 = 1. 0390
The approximate points are(0. 945 , 1 .102), (2. 139 , 1 .741), (2. 916 , 2 .157)
[It may not warrant this many significant figures, but it should make it easier to check your work.]